The recent push for the development of a “Smart Grid” will result in significant changes to the existing transmission and distribution networks, both in terms of the technology employed, as well as the manner in which the grid is operated. See, e.g., Energy Independence and Security Act of 2007, H.R. Res. 6, 110th Congress (2007) (enacted) (hereinafter “Energy Independence and Security Act of 2007”), the contents of which are hereby incorporated by reference in its entirety. These changes will result in new methods and opportunities for utilities and customers to control demand levels on the power grid. From the utility's perspective, advances in demand response capabilities through communication and automation improvements will lead to improved grid reliability through reduction in peak load and reduced congestion on the power lines. For the end-user, electricity costs will be reduced through better methods of planning and controlling their facility's electricity usage. To achieve this end, particularly with respect to this new level of customer involvement in the electricity market, better models and tools are needed to optimize the shifting, shedding, and overall control of a customer's electrical load.
For most commercial facilities, such as large office buildings, hotels, etc. the biggest percentage of electrical load is comprised of the lighting and HVAC systems. See, e.g., J. C. Lam, et al., An analysis of electricity end-use in air-conditioned office buildings in Hong Kong, Building and Environment, vol. 38, No. 3, pp. 493-498, March 2003, the contents of which are hereby incorporated by reference in its entirety. Appropriately controlling the HVAC systems can lead to significant savings. However, there are several challenges associated with HVAC controls, and therefore an accurate model is needed to realize the potential gains while minimizing any undesirable impacts, particularly the building comfort level. This comfort level is mainly directly related to temperature, among other ambient parameters (e.g. humidity, CO2 levels, etc.). To adequately dispatch a building's HVAC load, what is needed is a characterization of the relationship between the building thermal response and electrical demand. Static load models cannot capture the coupling that exists between building temperature and electric power sufficiently when it comes to demand response because of the long system time delays that come about due to this coupling. What is needed is an understanding of the load behavior during these response times.
Various methods of demand response have been in practice for many years. Existing demand response options can be grouped in 2 basic types: Price-Based options, such as Critical Peak Pricing (CPP), and Incentive-Based Programs, such as direct load control and load curtailment programs. See, e.g., US Department of Energy, Benefits of Demand Response in Electricity Markets and Recommendations for Achieving Them, Report to the United States Congress, February 2006 (hereinafter “Benefits of Demand Response”), the contents of which are hereby incorporated by reference in its entirety. It is desirable to advance these markets as part of the future “Smart Grid.” In order to accomplish this, it is also desirable to advance the tools being used to evaluate and control the demand side.
Traditionally in power systems, loads are represented in aggregate. Loads are grouped by bus, or substation, and modeled as one complex power injection of the form shown in (1).Siinj=Piinj+jQiinj  (1)where Siinj represents complex power, Piinj represents real power, and jQiinj represents reactive power.
While this structure is convenient in that it reduces model complexity when performing power system analysis, it is not appropriate for utilization in demand response. What is needed is an alternative approach that is better suited for demand response applications.